Study on application of ann - based mpc controllers for load-frequency control of an interconnected hydropower plant

 ( ), ( ), ( )
T
t t tie tiex t f t f t P t P t X t X t P t P t (3) 
u(t) is the input signal vector, 
1
2
( )
( )
( )
u t
u t
u t
 (4) 
D is the load disturbance vector, 
,1
,2
( )
( )
d
d
P t
D
P t
 (5)
Matrices of A, B, and F are corresponding to the matrices of state, input, and load 
disturbance. 
The output vector, y(t), is given as 
1 2 ,12( ) ( ), ( ),
T
tiey t f t f t P (6) 
and C denotes an identity matrix. The model mentioned above can be used efficiently in 
control solutions of the LFC. In this paper, both a single-area isolated and multi-area 
interconnected hydropower system models will be applied to validate the effectiveness of 
the proposed LFC strategies. 
3. ANN – BASED MPC FOR LFC 
3.1. An overview of ANN – based MPC 
In this section, we put forward the claim that artificial neural network (ANN) technique 
with its fast development recently has motivated researchers to apply for various control 
problems, including the LFC issue [9-11]. 
Model predictive control (MPC) is one of the most advanced control strategies which 
has been in use in the process industries. The application of the MPC in power system has 
been gained recently. Typically, the MPC, when integrated with the ANN, acts based on 
two phases: 
 (i) In the first phase, the control plant under consideration should be indentified by 
training a neural network. It means that such a neural network needs to be trained to 
represent the dynamics of the control plant. Typically, the neural network uses a training 
signal which can be calculated from the error between the plant output and the neural 
network output. It is evident the neural network can be trainned offline in batch mode, 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 89
using the previous inputs and previous plant outputs to predict future values of the plant 
output. 
(ii) In the second phase, namely predictive control, the receding horizon technique is 
used. The working principle is that the predictions of the neural network model are 
excecuted based upon a specified time horizon. It is found that a candidate of criterion 
over the specified horizon is taken for a numerical optimization program which should be 
used for the predictions. Considering the model predictive control process, it is evident the 
neural network plant model and the optimization block are integrated to form the 
controller. 
Governor
Hydro 
turbine
Generator
∆Pdi(t)
∆fi(t)
ith control - area 
f
g
NN 
model
System 
identification
NN 
model
Predictive 
control
Learning 
algorithm
Optimization 
mechanism
, ( )tie iP t 
( )if t 
Reference 
signal
ui(t)
1
2
ANN – based 
MPC
Figure 2. ANN-based MPC model applied to the ith control-area. 
The next section is to present the working principle of the ANN-based MPC under 
consideration applied to the LFC of a hydropower system. 
3.2. LFC Strategy Applying the ANN-based MPC 
This paper proposes two scenarios when applying the ANN-based MPC controller 
mentioned earlier to the LFC problem of a hydropower system. 
(i) Scenario 1: The ANN-based MPC is applied for a single-area isolated power system 
as shown in figure 3(a). 
(ii) Scenario 2: The ANN-based MPC – type LFC controller is applied for a two-area 
interconnected hydropower system as shown in figure 3(b). 
In both scenarios, this work proposes an optimization technique to determine an 
optimal gain for the scaling factor behind the MPC controller. A candidate of objective 
function of such an optimization technique applied for the ith control-area here is given 
below: 
,
,0
( ) .
T
i tie ij
i i j
J f t P dt
  (7) 
Using the above objective function, the proposed MPC-based LFC controller is able to 
obtain good control performance, which will be validated in the following section. 
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Study on application of ANN-based  hydropower plant.” 90 
Governor
Hydro 
turbine
Generator
∆PL
∆f
SINGLE-AREA ISOLATED 
HYDROPOWER PLANT
ANN – MPC
f
g k
Optimization 
mechanism
Objective 
function
(a)
Governor
Hydro 
turbine
Generator
∆PL1
Compute
∆Ptie12
Governor
Hydro 
turbine
Generator
∆PL2
ACE1(t) ∆f1
∆f2
CONTROL-AREA 1
CONTROL-AREA 2
ANN – MPC1
f
g k1
ACE2(t)
ANN – MPC2
f
g k2
Optimization 
mechanism
Objective 
function
(b)
Figure 3. Control structure of hydropower systems applying the LFC controllers. 
(a) Single – area isolated hydropower plant; 
(b) Two-area interconnected hydropower system. 
4. NUMERICAL SIMULATIONS TO VERIFY 
THE PROPOSED CONTROL STRATEGY 
We put forward the claim that it is necessary to execute simulation processes to 
validate the applicability of the proposed control strategy in dealing with the LFC problem 
of a hydropower system. This section considers two simulation cases: 
(1) First simulation case: Consider a single-area isolated hydropower system with a 
scenario of load change as shown in figure 5(a). A comparative simulation result between 
the proposed MPC-based LFC controller and the conventional PID-type LFC is 
represented in figure 5(b). 
(2) Second simulation case: Consider a two-area interconnected hydropower network 
with a scenario of load changes for two areas as shown in figure 6(a). This is a more 
practical simulation scenario of the load change, especially for the first area. It is apparent 
the load depending on users randomly and continuously changes in the first area is more 
suitable in practice. Simulation results for this perspective are represented in figures 6(b,c) 
and figure 7. It should be noted that the waveform of objective function is also depicted 
for both the PID and ANN-MPC LFC controllers for the comparative aim. The objective 
funtion is presented below: 
1 2 ,12( ) ( ) ( ) ( )obj tief t f t f t P t (8) 
To execute the ANN-MPC controller, we need to effectuate the controller configuration 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 91
following two steps as mentioned in Section 3. First, the plant identification must be 
implemented with parameters indicated in Appendix C. The results of this identification 
process are shown in figure 4. Next, in the second stage, the controller will be trained. 
Typical results of the training process for the ANN-based MPC are shown in figure 4. 
Figure 4. Training process of two ANN-based LFC controllers – typical results. 
From figures 5-7, it is clear the ANN-based MPC controller obtains much better control 
performances in comparison with the conventional PID regulator. To make a numerical 
comparison, let us consider four control cretiria as follows: 
0
( )
T
IAE ACE t dt (9) 
 
2
0
( )
T
ISE ACE t dt (10) 
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Study on application of ANN-based  hydropower plant.” 92 
0
( )
T
ITAE ACE t tdt (11) 
 
2
0
( )
T
ITSE ACE t tdt (12) 
The data achieved from the above four criteria are presented in Table 1. A closer look 
at the data revealed from figures 5-7 and Table 1 indicates that the proposed LFC control 
strategy based on ANN-MPC controllers obtains better control performance compared to 
the PID controller. This available evidence seems to claim that the proposed LFC 
controller should be a highly feasible control solution for the LFC problem of an 
interconnected hydropower system. 
Figure 5. Simulation results for the single-area hydropower plant. 
(a) Load change; 
(b) Dynamic response of the frequency deviation. 
P
d
PID
ANN-MPC
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 93
Figure 6. Simulation results for the two-area interconnected hydropower plant. 
(a) Load changes; 
(b) Frequency deviations of the first control-area; 
(c) Frequency deviations of the second control-area. 
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Study on application of ANN-based  hydropower plant.” 94 
Figure 7. Tie-line power interchange and objective function for the second simulation case. 
(a) Tie-line power flow; 
(b) Objective function. 
Table 1. Comparative results based on several control criteria 
in the second simulation case. 
5. CONCLUSION 
The findings studied in this paper provide confirmatory evidence that the proposed 
ANN-MPC-based LFC strategy is capable of solving effectively the LFC problem of an 
interconnected hydropower plant. Such an ANN-MPC controller is based on two typical 
stages of the working principle of the MPC controller. Furthermore, the scaling factors 
which are well-tuned by an optimization mechanism are applied to the ANN-MPC, 
gaining the applicability of the proposed control strategy. Current research seems to 
ti
e
PID
ANN-MPC
PID
ANN-MPC
Criteria PID MPC 
IAE (*10-3) 0.0378 0.0266 
ISE (*10-3) 0.0047 0.0034 
ITAE (*10-3) 7.4247 5.1596 
ITSE (*10-3) 0.8990 0.6432 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 95
validate the view that the LFC strategies are still to be improved in order to achieve better 
control performance, especially for looking a feasible LFC solution of a multi-area 
interconnected power system. Complicated large-scale electric power grids in co-operation 
with renewable energy sources should be significant control plants inspired by this study. 
APPENDICES 
Appendix A 
Nomenclature 
fn nominal frequency, fn = 50Hz 
f real frequency of the network, Hz 
tieP tie line power flow, p.u. 
∆f1,2 (t) frequency deviations of the first and second areas, in time domain, p.u. 
∆F1,2 (s) frequency deviations of the first and second areas, in Laplace domain, p.u. 
1,2 ( )ACE t Area control error, in time domain 
1 2( ), ( )u t u t control signal for the first and the second areas 
1,2dP load changes in the first and the second areas, p.u. 
,12tieP tie-line power flow deviation, p.u. 
,g iT time constant of governor, s 
,w iT time constant of hydro turbine unit, s 
Di
 load damping factor, p.u. MW/Hz 
Mi generator inertia constant, p.u. 
Tij
 tie-line time constant, sec 
Bi frequency bias factor, MW/p.u.Hz 
Ri speed regulation constant, Hz/MW 
,g iG transfer function of the governor unit 
,t iG transfer function of the hydro turbine unit 
,PiG transfer function of the rotor inertia and load (power system) 
Appendix B 
Two-area interconnected power system parameters: 
1 2 48.7g gT T s ; 1 2 1w wT T s 
1 2 1 2 1 2 1 2 120.513; 0.6; 1; 2.4; 0.0707;r rT T M M D D R R T 
Two simulation cases: 
Case 1: load change appears with three magnitutes of 0.05pu, 0.07pu and 0.03pu at 
three respective step times of 0s, 50s and 100s. 
Case 2: ∆PD1 is a uniform random number function generates uniformly distributed 
random numbers over an interval of [-0.05; 0.2] and a sample time of 10s. 
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Study on application of ANN-based  hydropower plant.” 96 
 ∆PD2 is a step function with a step time of 100s and the final value of 0.1pu. 
Appendix C 
Parameters to execute the ANN-based MPC are shown below: 
REFERENCES 
[1]. Kundur P. “Power system stability and control”. New York, USA: McGraw-Hill, 
1994. 
[2]. Shashi KP, Soumya RM, Nand K. “A literature survey on load-frequency control for 
conventional and distribution generation power systems”. Renewable and 
Sustainable Energy Reviews 2013; 25: 318-334. 
[3]. R. C. Dorf and R. H. Bishop, “Modern Control Systems”, Pearson Prentice Hall, 
2008. 
[4]. R. Verma, S. Pal and S. Sathans, “Intelligent Automatic Generation Control of Two-
Area Hydrothermal Power System Using ANN and Fuzzy Logic,” In: 2013 
International Conference on Communication Systems and Network Technologies 
(CSNT), pp. 552-556, 6-8 April 2013. 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 97
[5]. Hykin S. “Neural network”. USA: Mac Miller, 1994. 
[6]. Mohammad T. and Keigo W. “Intelligent Control Based on Flexible Neural 
Networks”. Springer, 1999. 
[7]. Norgaard M., Poulsen N. K., Hansen L. K., Ravn O. “Neural Networks for Modelling 
and Control of Dynamic Systems”. Springer, 2003. 
[8]. Ławryńczuk M. “Neural Networks in Model Predictive Control”. In: Nguyen N.T., 
Szczerbicki E. (eds) Intelligent Systems for Knowledge Management. Studies in 
Computational Intelligence, vol 252. Springer, Berlin, Heidelberg, 2009. 
[9]. Han, Hong-Gui & Zhang, Lu & Hou, Ying & Qiao, Jun-Fei. “Nonlinear Model 
Predictive Control Based on a Self-Organizing Recurrent Neural Network”. IEEE 
transactions on neural networks and learning systems, 2015. 27. 
10.1109/TNNLS.2015.2465174. 
[10]. Steven S. P. K., Aditya T., Bhushan G., Philip L. “A Deep Learning Architecture for 
Predictive Control”. IFAC PapersOnline 51-18, 2018, pp. 512 – 517. 
[11]. James B. R., David Q. M. and Moritz M. D. “Model Predictive Control: Theory, 
Computation and Design”, 2nd Edition, Nob Hill Publishing, LLC, 2019. 
TÓM TẮT 
NGHIÊN CỨU ỨNG DỤNG ĐIỀU KHIỂN DỰ BÁO DỰA TRÊN 
TRÍ TUỆ NHÂN TẠO CHO BÀI TOÁN ĐIỀU KHIỂN TẦN SỐ - PHỤ TẢI 
NHÀ MÁY THỦY ĐIỆN ĐA KẾT NỐI 
Trong thị trường điện Việt Nam hiện nay, thủy điện vẫn chiếm một tỷ trọng lớn 
(khoảng 38%). Do đó, việc nghiên cứu các vấn đề điều khiển trong nhà máy thủy 
điện có ý nghĩa vô cùng lớn. Chiến lược điều khiển tần số-phụ tải là một trong số 
những bài toán điều khiển đặc biệt quan tâm. Mục tiêu chính của bài toán điều 
khiển này khi phụ tải lưới điện thay đổi liên tục và ngẫu nhiên là kiểm soát tần số 
lưới điện xung quanh giá trị danh định (ở Việt Nam là 50Hz) và công suất thực trao 
đổi trên đường dây cân bằng với công suất đã lên lịch trình trước. Việc này đảm 
bảo sự ổn định của hệ thống các nhà máy thủy điện đa kết nối nói riêng và hệ thống 
điện quốc gia nói chung. Bài báo này đề xuất một giải pháp điều khiển dự báo dựa 
trên mạng trí tuệ nhân tạo cho bài toán điều khiển tần số - phụ tải của nhà máy thủy 
điện. Chiến lược điều khiển này kết hợp với các hệ số chỉnh định có được từ một 
thuật toán tối ưu đã trở thành một giải pháp khả thi cho bài toán điều khiển tần số - 
phụ tải. Cùng với các kết quả mô phỏng số đã đạt được trong nghiên cứu này, ta có 
thể khẳng định tính khả thi của việc ứng dụng giải pháp điều khiển dự báo dựa trên 
mạng trí tuệ nhân tạo đã đề xuất cho bài điều khiển tần số - phụ tải của một hệ 
thống thủy điện đa kết nối. 
Từ khóa: ANN; MPC; LFC; Hệ thống thủy điện đa kết nối; Thay đổi phụ tải; Độ lệch tần số lưới; Công suất 
trao đổi. 
Received date, 10th December, 2019 
Revised manuscript, 10th January, 2020 
Published, 12th February, 2020 
Author affiliations: 
 1 Electric Power University; 
 2 National Center for Technological Progress; 
 3 University of Transport and Communications. 
 *Corresponding author: trungnd@epu.edu.vn.